DEMinSoCAL

This does NOT fix it.  It's a myth.  It was suggested like a year or two ago and almost immediately debunked because while it may SEEM like it fixes it, the slow startup comes right back after some time (as is the case anyways due to the fact the slow startup is actually due to the macOS security system, not some obscure display setting).  Check back in after a couple weeks and let us know if it still is working for you (it didn't for me a long time ago when I tried the "trick").
App startup time WILL be fast for a number of times until one restarts their Mac at which time it may decide to slow again.

Looks like the fix comes with price tag 50€ … thanks

Buy lottery tickets.  You have a better chance of winning the lottery than Serif/Affinity fixing the app. 

Buy lottery tickets.  You have a better chance of winning the lottery than Serif/Affinity fixing the app. 

Only Mac related.

Thank you @Patrick Connor for this workaround. This worked for all three applications, both MAS (Photo and Designer) and non-MAS (Publisher). Very thankful for this.
It is good to hear something again from Serif after a long silence. But please don't try to make this an Apple problem (see my other post as example). No other unified apps (and there are many by now) have shown similar behaviour, and the problem occurs with both MAS and non-MAS versions. There could very well be something on Apple's side that attenuates the issue, but Serif owns this problem. And from your messages it looks like Serif still has no idea what the issue is, hasn't solved it in a new release, can't replicate the issue for non-MAS versions, and found a workaround purely by accident. As happy as I am with the workaround, it has not taken away my concerns on Serif's abilities to solve problems.  

Well count me in on slow starting of web downloaded versions.  After the MAS versions started slowing, I downloaded trials of the 3 apps from your website.  Those worked for a couple weeks then went slow.  I know they were the trial versions because those were the ones I had in my dock.
FWIW, the copy app kludge seems to work after doing preliminary trials.  Interesting, though, that other apps (like Pixelmator Pro, AppleSilicon/App Store version) do not exhibit slow starting at all. 

Are there any updates from Serif on this issue, e.g. has the cause been identified?
I'd also like to confirm this problem isn't limited to the MAS versions, as the issue occurs for me with the latest web versions of Photo and Designer.

Has Serif laid off all their staff? Are they going out of business? Two months since their last update and nothing on this issue?
I hope they are not wasting time on new features. There's just too much that needs to be fixed, like these extended start-up bounces and keeping track of what brush you're using when you make minor changes like brush size.

Of course, there are many reports of the startup delay affecting the web-versions of the app.  I, for one, reported that while I purchased the App Store versions of all the apps and all were displaying the start delay, I also then downloaded trial version from your web-store and while at first they started normally, in a couple weeks they also started to display the start delay similar to the App Store versions.  I removed the trials as they were no better than the App Store at that point.
Given it's been 2 months since this started and you're "still investigating", it sounds like it's not a high priority for your team.

That is a known problem.  There is a thread about it here:
However, although it's been a known problem for over a month, the team at Affinity have not fixed it.  

FWIW, my website-downloaded versions worked normally for 2 weeks then suddenly had delayed startup.  Seems neither app-store or website versions are immune.

Every single one of my apps are Universal, except for one.  I've made a point of installing only Universal versions (including a beta of the Universal version of Microsoft 365 apps), and none of them have this issue.
I'm not a developer so I don't know how the process works, but there must be a difference in the code between the App Store version and the standalone version.  I see the size of the file is different, so they are not the same.  
In any case, I'm stuck on using a trial (which is temporary) so please don't sit back and wait to see if others have the same issue.  You have two people with the problem.  I'm happy to assist in troubleshooting, or...you could actually download the Universal app from the App Store on a M1-based Mac and try it yourself.

I am not using WIFI.  I use Ethernet.  But even with it unplugged (no internet), it is the same -- slow startup.